a uranium-238 nucleus may stay in one piece for billions of years, but later it decays into an a particle of mass 6.64 x 10^-27 and a thorium-234 nucleus of mass 3.88 x 10^-25. The decay process itself is extremely fast (about 10^-20 s).

Suppose the uranium nucleus was at rest just before the decay. If the a particle is emitted at a speed of 1.4 x 10^7 m/s, what would be the recoil speed of the thorium nucleus?